Errata and Clarifications for Second Printing of
Introduction to Stochastic Search and Optimization:
Estimation, Simulation, and Control
by J. C. Spall
© John Wiley and Sons, Inc., 2003
Please provide corrections or suggestions to James C. Spall. To determine if a copy of the book
is the second printing check the last digit at the bottom of page iv near the front.
CHAPTER 4
p. 107, lines 7 − 9 of Condition B.2: δ(η) and δ0 should be constrained to be strictly positive.
Hence the relevant statements should read: “....there exists a δ(η) > 0 such that....” and “....there
exists a δ0 > 0 such that....”
CHAPTER 6
p. 169, line 9: The ratio of maximum eigenvalue to minimum eigenvalue is approximately 175,
not 65.
CHAPTER 9
p. 251, line 7 of Example 9.4: The ratio of maximum eigenvalue to minimum eigenvalue is
approximately 175, not 65 (same correction appears in Chapter 6, as mentioned above).
CHAPTER 10
p. 270 (paragraphs 2 and 3): Several modifications to the discussion are required to
accommodate the fact that the Markov chain is not irreducible (because a GA with elitism cannot
move to a population whose best fitness value is lower than the current best value). However, the
key conclusion discussed in the current text is unchanged: namely, the chain does have a unique
limiting value pT with ∑ i∈J pi = 1 because the GA is always saving the best chromosome
encountered.
CHAPTER 13
p. 332: The third line of eqn. (13.1) should have a minus (not plus) sign at the beginning. Hence
the line should read: −2 [ h(θ, x ) − E ( z | x ) ] E [( z − E ( z | x ) ) x ] . This change does not affect the
last (fourth) line of the equation.
p. 344: In the fourth line of the second full paragraph, “... n nT values for MSE(m)...” should be
replaced by “...multiple values for MSE(m)...”
p. 353: The first integral in the second line of the equation at the top of the page should read
∂ 2 log l
∫ ∂θ∂θT
l dζ , not
∂ log 2 l
∫ ∂θ∂θT
l dζ .
CHAPTER 14
Exercise 14.13 (clarification): The second sentence should reflect that the diagonals in the
covariance matrix are unity (as indicated by the first sentence where the reader is instructed to
build on the setting of Exercise 14.12) while the off-diagonals are 0.5. Hence, the second
sentence should read: “In the simulated indifference zone selection process, assume that
cov[yk(θi), yk(θj)] = 0.5 for all k and i ≠ j.”
CHAPTER 15
pp. 429−430 (clarification to Example 15.7): Note that Q(θ, V) is a sum of a part dependent on
V and a part independent of V (i.e., Q(θ, V) = V + b θ ). In this and other such cases, it is only
necessary to apply the sample path averaging based on V0, V1,…, VN−1 to the part dependent on
V. Hence, (15.16) can be re-expressed as
LN (θ) =
1
N
N −1
∑ Vi
i =0
pV (Vi θ) b
+ ,
pV (Vi θ′) θ
from which the expression for ∂LN (θ) ∂θ in (15.17) directly follows.
CHAPTER 16
p. 440: The displayed integral should be set equal to 1 as in:
∫ q(w | X = x) dw
= 1. Further, in
the fourth and fifth lines below this displayed integral, f (x) should be p(x) (two instances) and
the associated 0 should be 0 (nonbold) since p(x) is a scalar function. Hence, the relevant part of
the lines should read: “...of points where p(x) ≠ 0, should be a superset of the set of points x
where p(x) ≠ 0.”
APPENDIX B
pp. 516−517 (clarification): The basic one-sample results of Section B.1 are not restricted to
only the μ = 0 case (although this is the case of interest when applying these results to the twosample setting of interest in Section B.2).